∃∃K1. ⬇*[b, f] L1 ≡ K1 & G ⊢ K1 ⫃[RP] K2.
#RP #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
-| #I #L1 #L2 #V #HL12 #IH #b #f #K2 #Hf #H
- elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
+| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
+ elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
[ #Hf #H destruct -IH
- /3 width=3 by lsubc_pair, drops_refl, ex2_intro/
+ /3 width=3 by lsubc_bind, drops_refl, ex2_intro/
| #g #Hg #HLK2 #H destruct -HL12
elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
]
| #L1 #L2 #V #W #A #HV #H1W #H2W #HL12 #IH #b #f #K2 #Hf #H
- elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
+ elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
[ #Hf #H destruct -IH
/3 width=8 by drops_refl, lsubc_beta, ex2_intro/
| #g #Hg #HLK2 #H destruct -HL12
#RR #RS #RP #HR #b #f #G #L1 #K1 #H elim H -f -L1 -K1
[ #f #Hf #Y #H lapply (lsubc_inv_atom1 … H) -H
#H destruct /4 width=3 by lsubc_atom, drops_atom, ex2_intro/
-| #f #I #L1 #K1 #V1 #_ #IH #K2 #HK12 elim (IH … HK12) -K1
- /3 width=5 by lsubc_pair, drops_drop, ex2_intro/
-| #f #I #L1 #K1 #V1 #V2 #HLK1 #HV21 #IH #X #H elim (lsubc_inv_pair1 … H) -H *
+| #f #I #L1 #K1 #_ #IH #K2 #HK12 elim (IH … HK12) -K1
+ /3 width=5 by lsubc_bind, drops_drop, ex2_intro/
+| #f #Z #I #L1 #K1 #HLK1 #HZ #IH #Y #H elim (lsubc_inv_bind1 … H) -H *
[ #K2 #HK12 #H destruct -HLK1
- elim (IH … HK12) -K1 /3 width=5 by lsubc_pair, drops_skip, ex2_intro/
- | #K2 #V #W2 #A #HV #H1W2 #H2W2 #HK12 #H1 #H2 #H3 destruct
+ elim (IH … HK12) -K1 /3 width=5 by lsubc_bind, drops_skip, ex2_intro/
+ | #K2 #V2 #W2 #A #HV2 #H1W2 #H2W2 #HK12 #H1 #H2 destruct
+ elim (liftsb_inv_pair_sn … HZ) -HZ #V1 #HV21 #H destruct
elim (lifts_inv_flat1 … HV21) -HV21 #W3 #V3 #HW23 #HV3 #H destruct
elim (IH … HK12) -IH -HK12 #K #HL1K #HK2
- lapply (acr_lifts … HR … HV … HLK1 … HV3) -HV
+ lapply (acr_lifts … HR … HV2 … HLK1 … HV3) -HV2
lapply (acr_lifts … HR … H1W2 … HLK1 … HW23) -H1W2
- /4 width=10 by lsubc_beta, aaa_lifts, drops_skip, ex2_intro/
+ /4 width=10 by lsubc_beta, aaa_lifts, drops_skip, ext2_pair, ex2_intro/
]
]
qed-.